Admissible heuristic

About: Admissible heuristic is a research topic. Over the lifetime, 197 publications have been published within this topic receiving 15329 citations. The topic is also known as: admissible heuristics.

Goal-oriented Euclidean heuristics with manifold learning

Abstract: Recently, a Euclidean heuristic (EH) has been proposed for A* search. EH exploits manifold learning methods to construct an embedding of the state space graph, and derives an admissible heuristic distance between two states from the Euclidean distance between their respective embedded points. EH has shown good performance and memory efficiency in comparison to other existing heuristics such as differential heuristics. However, its potential has not been fully explored. In this paper, we propose a number of techniques that can significantly improve the quality of EH. We propose a goal-oriented manifold learning scheme that optimizes the Euclidean distance to goals in the embedding while maintaining admissibility and consistency. We also propose a state heuristic enhancement technique to reduce the gap between heuristic and true distances. The enhanced heuristic is admissible but no longer consistent. We then employ a modified search algorithm, known as B′ algorithm, that achieves optimality with inconsistent heuristics using consistency check and propagation. We demonstrate the effectiveness of the above techniques and report un-matched reduction in search costs across several non-trivial benchmark search problems.

Generating admissible heuristics by abstraction for search in stochastic domains

Abstract: Search in abstract spaces has been shown to produce useful admissible heuristic estimates in deterministic domains. We show in this paper how to generalize these results to search in stochastic domains. Solving stochastic optimization problems is significantly harder than solving their deterministic counterparts. Designing admissible heuristics for stochastic domains is also much harder. Therefore, deriving such heuristics automatically using abstraction is particularly beneficial. We analyze this approach both theoretically and empirically and show that it produces significant computational savings when used in conjunction with the heuristic search algorithm LAO*.

On the Optimal Efficiency of Cost-Algebraic A*

Abstract: Edelkamp et al. (2005) proved that A*, given an admissible heuristic, is guaranteed to return an optimal solution in any cost algebra, not just in the traditional shortest path setting. In this paper, we investigate cost-algebraic A*’s optimal efficiency: in the cost-algebraic setting, under what conditions is A* guaranteed to expand the fewest possible states? In the traditional setting, this question was examined in detail by Dechter & Pearl (1985). They identified five different situations in which A* was optimally efficient. We show that three of them continue to hold in the cost-algebraic setting, but that one does not. We also show that one of them is false, it does not hold even in the traditional setting. We introduce an alternative that does hold in the cost-algebraic setting. Finally, we show that a well-known result due to Nilsson does not hold in the general cost-algebraic setting but does hold in a slightly less general setting.

Near-optimal search in continuous domains

Abstract: We investigate search problems in continuous state and action spaces with no uncertainty Actions have costs and can only be taken at discrete time steps (unlike the case with continuous control) Given an admissible heuristic function and a starting state, the objective is to find a minimum-cost plan that reaches a goal state As the continuous domain does not allow the tight optimality results that are possible in the discrete case (for example by A*), we instead propose and analyze an approximate forward-search algorithm that has the following provable properties Given a desired accuracy E, and a bound d on the length of the plan, the algorithm computes a lower bound L on the cost of any plan It either (a) returns a plan of cost L that is at most E more than the optimal plan, or (b) if, according to the heuristic estimate, there may exist a plan of cost L of length > d, returns a partial plan that traces the first d steps of such plan To our knowledge, this is the first algorithm that provides optimality guarantees in continuous domains with discrete control and without uncertainty

A Heuristic for Hybrid Planning with Preferences.

Abstract: In this paper, we introduce an admissible heuristic for hybrid planning with preferences. Hybrid planning is the fusion of hierarchical task network (HTN) planning with partial order causal link (POCL) planning. We consider preferences to be soft goals — facts one would like to see satisfied in a goal state, but which do not have to hold necessarily. Our heuristic estimates the best quality of any solution that can be developed from the current plan under consideration. It can thus be used by any branch-and-bound algorithm that performs search in the space of plans to prune suboptimal plans from the search space.